This is an notebook containing code for generating plots for our talk at Cogsci 2018 (Madison, WI). The corresponding proceedings paper is here in PDF form, and here in .Rmd form.

EFA calculations

Older children (7-9y)

Factor Analysis with confidence intervals using method = psych::fa(r = d_old_wide, nfactors = nfactors_old, n.iter = n_iter, 
    rotate = chosen_rot, cor = chosen_cor)
Factor Analysis using method =  minres
Call: psych::fa(r = d_old_wide, nfactors = nfactors_old, n.iter = n_iter, 
    rotate = chosen_rot, cor = chosen_cor)
Standardized loadings (pattern matrix) based upon correlation matrix
              factor1 factor2 factor3   h2   u2 com
hunger           0.98   -0.12    0.02 0.87 0.13 1.0
smell            0.77   -0.09    0.06 0.58 0.42 1.0
fear             0.77    0.23   -0.02 0.81 0.19 1.2
pain             0.72    0.18   -0.02 0.67 0.33 1.1
fatigue          0.50    0.24    0.25 0.62 0.38 1.9
nausea           0.48   -0.01    0.16 0.30 0.70 1.2
anger            0.42    0.41    0.14 0.62 0.38 2.2
guilt           -0.11    0.80   -0.05 0.55 0.45 1.0
embarrassment   -0.16    0.75    0.11 0.52 0.48 1.1
pride            0.16    0.69    0.02 0.63 0.37 1.1
hurt_feelings    0.06    0.68    0.03 0.52 0.48 1.0
sadness          0.20    0.65    0.03 0.60 0.40 1.2
love             0.32    0.50   -0.05 0.48 0.52 1.7
happiness        0.40    0.41    0.01 0.49 0.51 2.0
figuring_out     0.04   -0.10    0.74 0.53 0.47 1.0
choice           0.06    0.09    0.72 0.61 0.39 1.0
memory          -0.17    0.05    0.71 0.46 0.54 1.1
temperature      0.04   -0.06    0.64 0.41 0.59 1.0
depth            0.03   -0.04    0.55 0.30 0.70 1.0
awareness        0.10    0.11    0.52 0.37 0.63 1.2

                      factor1 factor2 factor3
SS loadings              4.27    3.81    2.86
Proportion Var           0.21    0.19    0.14
Cumulative Var           0.21    0.40    0.55
Proportion Explained     0.39    0.35    0.26
Cumulative Proportion    0.39    0.74    1.00

 With factor correlations of 
        factor1 factor2 factor3
factor1    1.00    0.49    0.36
factor2    0.49    1.00    0.29
factor3    0.36    0.29    1.00

Mean item complexity =  1.3
Test of the hypothesis that 3 factors are sufficient.

The degrees of freedom for the null model are  190  and the objective function was  12.3 with Chi Square of  1408.65
The degrees of freedom for the model are 133  and the objective function was  1.71 

The root mean square of the residuals (RMSR) is  0.04 
The df corrected root mean square of the residuals is  0.05 

The harmonic number of observations is  123 with the empirical chi square  81.59  with prob <  1 
The total number of observations was  123  with Likelihood Chi Square =  192.49  with prob <  0.00057 

Tucker Lewis Index of factoring reliability =  0.929
RMSEA index =  0.068  and the 90 % confidence intervals are  0.04 0.079
BIC =  -447.53
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy             
                                                  factor1 factor2 factor3
Correlation of (regression) scores with factors      0.97    0.94    0.92
Multiple R square of scores with factors             0.95    0.89    0.85
Minimum correlation of possible factor scores        0.90    0.78    0.69

 Coefficients and bootstrapped confidence intervals 
                low factor1 upper   low factor2 upper   low factor3 upper
hunger         0.83    0.98  1.05 -0.16   -0.12  0.04 -0.06    0.02  0.17
smell          0.61    0.77  0.89 -0.22   -0.09  0.09 -0.05    0.06  0.19
fear           0.68    0.77  0.95  0.10    0.23  0.37 -0.16   -0.02  0.07
pain           0.51    0.72  0.92  0.08    0.18  0.37 -0.10   -0.02  0.09
fatigue        0.32    0.50  0.75  0.11    0.24  0.36  0.13    0.25  0.38
nausea         0.34    0.48  0.65 -0.18   -0.01  0.09  0.02    0.16  0.30
anger          0.19    0.42  0.61  0.21    0.41  0.67  0.01    0.14  0.34
guilt         -0.21   -0.11  0.07  0.62    0.80  0.91 -0.13   -0.05  0.04
embarrassment -0.27   -0.16  0.02  0.63    0.75  0.86  0.02    0.11  0.19
pride         -0.03    0.16  0.28  0.59    0.69  0.87 -0.10    0.02  0.13
hurt_feelings -0.09    0.06  0.32  0.47    0.68  0.84 -0.10    0.03  0.14
sadness        0.03    0.20  0.41  0.48    0.65  0.81 -0.10    0.03  0.21
love           0.13    0.32  0.60  0.30    0.50  0.68 -0.29   -0.05  0.09
happiness      0.23    0.40  0.54  0.33    0.41  0.54 -0.09    0.01  0.20
figuring_out  -0.05    0.04  0.17 -0.23   -0.10  0.03  0.55    0.74  0.85
choice        -0.05    0.06  0.19 -0.11    0.09  0.24  0.55    0.72  0.91
memory        -0.35   -0.17  0.06 -0.19    0.05  0.33  0.63    0.71  0.77
temperature   -0.13    0.04  0.15 -0.17   -0.06  0.10  0.49    0.64  0.81
depth         -0.13    0.03  0.26 -0.40   -0.04  0.23  0.34    0.55  0.70
awareness     -0.04    0.10  0.32  0.00    0.11  0.29  0.38    0.52  0.63

 Interfactor correlations and bootstrapped confidence intervals 
            lower estimate upper
fctr1-fctr2 0.368     0.49  0.56
fctr1-fctr3 0.193     0.36  0.40
fctr2-fctr3 0.031     0.29  0.48

Younger children (4-6y)

Factor Analysis with confidence intervals using method = psych::fa(r = d_young_wide, nfactors = nfactors_young, n.iter = n_iter, 
    rotate = chosen_rot, cor = chosen_cor)
Factor Analysis using method =  minres
Call: psych::fa(r = d_young_wide, nfactors = nfactors_young, n.iter = n_iter, 
    rotate = chosen_rot, cor = chosen_cor)
Standardized loadings (pattern matrix) based upon correlation matrix
              factor1 factor2 factor3   h2   u2 com
anger            0.87   -0.11   -0.03 0.63 0.37 1.0
hunger           0.59    0.18    0.08 0.58 0.42 1.2
hurt_feelings    0.58    0.13    0.04 0.46 0.54 1.1
smell            0.55    0.12    0.01 0.40 0.60 1.1
fatigue          0.54    0.09    0.21 0.54 0.46 1.4
sadness          0.47    0.27   -0.06 0.40 0.60 1.6
nausea           0.46    0.28    0.00 0.44 0.56 1.7
pain             0.44    0.11    0.06 0.30 0.70 1.2
happiness        0.01    0.78    0.07 0.67 0.33 1.0
love            -0.01    0.76   -0.02 0.56 0.44 1.0
pride            0.22    0.51    0.07 0.49 0.51 1.4
fear             0.27    0.36    0.09 0.37 0.63 2.0
embarrassment    0.21    0.31    0.14 0.31 0.69 2.3
temperature     -0.12    0.06    0.77 0.55 0.45 1.1
memory           0.02    0.00    0.54 0.30 0.70 1.0
depth            0.15   -0.08    0.49 0.30 0.70 1.3
guilt            0.13    0.05    0.48 0.34 0.66 1.2
figuring_out     0.33   -0.14    0.45 0.37 0.63 2.0
choice           0.06    0.26    0.37 0.33 0.67 1.8
awareness        0.23    0.07    0.35 0.30 0.70 1.8

                      factor1 factor2 factor3
SS loadings              3.75    2.58    2.32
Proportion Var           0.19    0.13    0.12
Cumulative Var           0.19    0.32    0.43
Proportion Explained     0.43    0.30    0.27
Cumulative Proportion    0.43    0.73    1.00

 With factor correlations of 
        factor1 factor2 factor3
factor1    1.00    0.58    0.50
factor2    0.58    1.00    0.46
factor3    0.50    0.46    1.00

Mean item complexity =  1.4
Test of the hypothesis that 3 factors are sufficient.

The degrees of freedom for the null model are  190  and the objective function was  8.81 with Chi Square of  1017.87
The degrees of freedom for the model are 133  and the objective function was  1.69 

The root mean square of the residuals (RMSR) is  0.05 
The df corrected root mean square of the residuals is  0.06 

The harmonic number of observations is  122 with the empirical chi square  129.66  with prob <  0.57 
The total number of observations was  124  with Likelihood Chi Square =  192.34  with prob <  0.00059 

Tucker Lewis Index of factoring reliability =  0.895
RMSEA index =  0.068  and the 90 % confidence intervals are  0.04 0.078
BIC =  -448.76
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                  factor1 factor2 factor3
Correlation of (regression) scores with factors      0.93    0.92    0.89
Multiple R square of scores with factors             0.87    0.84    0.79
Minimum correlation of possible factor scores        0.75    0.68    0.58

 Coefficients and bootstrapped confidence intervals 
                low factor1 upper   low factor2 upper   low factor3 upper
anger          0.54    0.87  1.22 -0.55   -0.11  1.20 -0.27   -0.03  0.37
hunger         0.18    0.59  1.33  0.20    0.18  0.88 -0.17    0.08  0.40
hurt_feelings  0.43    0.58  1.09 -0.37    0.13  1.29 -0.24    0.04  0.38
smell          0.14    0.55  1.20  0.13    0.12  0.84 -0.20    0.01  0.27
fatigue        0.04    0.54  1.34 -0.19    0.09  1.04 -0.05    0.21  0.58
sadness        0.32    0.47  1.07 -0.08    0.27  1.12 -0.14   -0.06  0.17
nausea         0.02    0.46  1.32  0.05    0.28  1.11 -0.16    0.00  0.25
pain           0.17    0.44  0.81 -0.08    0.11  0.88 -0.11    0.06  0.40
happiness      0.05    0.01  1.01  0.41    0.78  1.20 -0.12    0.07  0.28
love           0.02   -0.01  0.86  0.44    0.76  1.17 -0.18   -0.02  0.30
pride          0.02    0.22  1.07  0.26    0.51  1.15 -0.11    0.07  0.34
fear          -0.08    0.27  0.99  0.14    0.36  1.12 -0.13    0.09  0.36
embarrassment -0.07    0.21  0.88  0.02    0.31  0.95 -0.07    0.14  0.42
temperature   -0.35   -0.12  0.43 -0.22    0.06  0.28  0.47    0.77  0.92
memory        -0.32    0.02  0.46 -0.31    0.00  0.56  0.31    0.54  0.70
depth         -0.16    0.15  0.58 -0.45   -0.08  0.52  0.20    0.49  0.82
guilt         -0.12    0.13  0.67 -0.25    0.05  0.67  0.22    0.48  0.65
figuring_out   0.07    0.33  0.78 -0.49   -0.14  0.70  0.10    0.45  0.76
choice        -0.11    0.06  0.68  0.11    0.26  0.56  0.08    0.37  0.63
awareness     -0.03    0.23  0.73 -0.60    0.07  1.12 -0.02    0.35  0.79

 Interfactor correlations and bootstrapped confidence intervals 
            lower estimate upper
fctr1-fctr2  0.41     0.58  0.63
fctr1-fctr3  0.17     0.50  0.52
fctr2-fctr3  0.20     0.46  0.42
Factor Analysis with confidence intervals using method = psych::fa(r = d_young_wide, nfactors = 2, n.iter = n_iter, rotate = chosen_rot, 
    cor = chosen_cor)
Factor Analysis using method =  minres
Call: psych::fa(r = d_young_wide, nfactors = 2, n.iter = n_iter, rotate = chosen_rot, 
    cor = chosen_cor)
Standardized loadings (pattern matrix) based upon correlation matrix
              factor1 factor2   h2   u2 com
hunger           0.72    0.05 0.57 0.43 1.0
nausea           0.70   -0.04 0.45 0.55 1.0
happiness        0.69    0.01 0.48 0.52 1.0
sadness          0.69   -0.10 0.40 0.60 1.0
pride            0.67    0.01 0.46 0.54 1.0
anger            0.67    0.00 0.45 0.55 1.0
love             0.66   -0.08 0.37 0.63 1.0
hurt_feelings    0.65    0.02 0.44 0.56 1.0
smell            0.63   -0.02 0.39 0.61 1.0
fear             0.58    0.04 0.37 0.63 1.0
fatigue          0.58    0.20 0.52 0.48 1.2
pain             0.51    0.04 0.29 0.71 1.0
embarrassment    0.48    0.10 0.30 0.70 1.1
temperature     -0.07    0.76 0.52 0.48 1.0
memory           0.00    0.55 0.30 0.70 1.0
depth            0.05    0.52 0.30 0.70 1.0
guilt            0.15    0.48 0.34 0.66 1.2
figuring_out     0.17    0.46 0.34 0.66 1.3
awareness        0.26    0.36 0.31 0.69 1.8
choice           0.28    0.34 0.31 0.69 1.9

                      factor1 factor2
SS loadings              5.73    2.16
Proportion Var           0.29    0.11
Cumulative Var           0.29    0.39
Proportion Explained     0.73    0.27
Cumulative Proportion    0.73    1.00

 With factor correlations of 
        factor1 factor2
factor1     1.0     0.6
factor2     0.6     1.0

Mean item complexity =  1.1
Test of the hypothesis that 2 factors are sufficient.

The degrees of freedom for the null model are  190  and the objective function was  8.81 with Chi Square of  1017.87
The degrees of freedom for the model are 151  and the objective function was  2.12 

The root mean square of the residuals (RMSR) is  0.06 
The df corrected root mean square of the residuals is  0.07 

The harmonic number of observations is  122 with the empirical chi square  176.89  with prob <  0.074 
The total number of observations was  124  with Likelihood Chi Square =  242.27  with prob <  3.5e-06 

Tucker Lewis Index of factoring reliability =  0.859
RMSEA index =  0.077  and the 90 % confidence intervals are  0.053 0.086
BIC =  -485.59
Fit based upon off diagonal values = 0.97
Measures of factor score adequacy             
                                                  factor1 factor2
Correlation of (regression) scores with factors      0.95    0.89
Multiple R square of scores with factors             0.91    0.79
Minimum correlation of possible factor scores        0.82    0.58

 Coefficients and bootstrapped confidence intervals 
                low factor1 upper   low factor2 upper
hunger         0.62    0.72  0.96 -0.61    0.05  1.21
nausea         0.35    0.70  1.05 -0.41   -0.04  0.93
happiness      0.21    0.69  1.09 -0.29    0.01  0.92
sadness        0.45    0.69  0.92 -0.36   -0.10  0.59
pride          0.38    0.67  0.91 -0.36    0.01  1.09
anger          0.46    0.67  0.93 -0.54    0.00  0.96
love           0.18    0.66  1.03 -0.48   -0.08  0.84
hurt_feelings  0.34    0.65  0.97 -0.26    0.02  0.91
smell          0.46    0.63  0.85 -0.72   -0.02  1.00
fear           0.43    0.58  0.89 -0.51    0.04  0.94
fatigue        0.40    0.58  1.02 -0.29    0.20  1.10
pain           0.26    0.51  0.83 -0.41    0.04  1.07
embarrassment  0.22    0.48  0.86 -0.29    0.10  0.94
temperature   -0.36   -0.07  0.86  0.68    0.76  0.93
memory        -0.14    0.00  0.68  0.04    0.55  0.97
depth         -0.24    0.05  0.80  0.19    0.52  0.85
guilt         -0.01    0.15  0.73  0.11    0.48  0.93
figuring_out   0.03    0.17  0.79 -0.13    0.46  1.21
awareness     -0.06    0.26  0.77 -0.06    0.36  1.11
choice         0.02    0.28  0.81 -0.01    0.34  0.97

 Interfactor correlations and bootstrapped confidence intervals 
            lower estimate upper
fctr1-fctr2  0.35      0.6  0.66
Factor Analysis with confidence intervals using method = psych::fa(r = d_young_wide, nfactors = 1, n.iter = n_iter, rotate = chosen_rot, 
    cor = chosen_cor)
Factor Analysis using method =  minres
Call: psych::fa(r = d_young_wide, nfactors = 1, n.iter = n_iter, rotate = chosen_rot, 
    cor = chosen_cor)
Standardized loadings (pattern matrix) based upon correlation matrix
              factor1   h2   u2 com
hunger           0.74 0.55 0.45   1
fatigue          0.72 0.52 0.48   1
happiness        0.68 0.46 0.54   1
pride            0.66 0.44 0.56   1
anger            0.65 0.43 0.57   1
hurt_feelings    0.65 0.42 0.58   1
nausea           0.65 0.42 0.58   1
smell            0.60 0.36 0.64   1
fear             0.60 0.36 0.64   1
sadness          0.60 0.36 0.64   1
love             0.58 0.34 0.66   1
embarrassment    0.55 0.30 0.70   1
choice           0.53 0.28 0.72   1
pain             0.53 0.28 0.72   1
awareness        0.52 0.27 0.73   1
figuring_out     0.51 0.26 0.74   1
guilt            0.50 0.25 0.75   1
temperature      0.49 0.24 0.76   1
depth            0.43 0.19 0.81   1
memory           0.41 0.17 0.83   1

               factor1
SS loadings       6.90
Proportion Var    0.35

Mean item complexity =  1
Test of the hypothesis that 1 factor is sufficient.

The degrees of freedom for the null model are  190  and the objective function was  8.81 with Chi Square of  1017.87
The degrees of freedom for the model are 170  and the objective function was  2.59 

The root mean square of the residuals (RMSR) is  0.08 
The df corrected root mean square of the residuals is  0.08 

The harmonic number of observations is  122 with the empirical chi square  269.99  with prob <  1.6e-06 
The total number of observations was  124  with Likelihood Chi Square =  297.95  with prob <  4.7e-09 

Tucker Lewis Index of factoring reliability =  0.826
RMSEA index =  0.084  and the 90 % confidence intervals are  0.063 0.093
BIC =  -521.5
Fit based upon off diagonal values = 0.95
Measures of factor score adequacy             
                                                  factor1
Correlation of (regression) scores with factors      0.96
Multiple R square of scores with factors             0.92
Minimum correlation of possible factor scores        0.84

 Coefficients and bootstrapped confidence intervals 
               low factor1 upper
hunger        0.68    0.74  0.84
fatigue       0.60    0.72  0.81
happiness     0.57    0.68  0.82
pride         0.55    0.66  0.78
anger         0.50    0.65  0.77
hurt_feelings 0.53    0.65  0.80
nausea        0.56    0.65  0.75
smell         0.45    0.60  0.80
fear          0.51    0.60  0.73
sadness       0.50    0.60  0.72
love          0.52    0.58  0.70
embarrassment 0.46    0.55  0.70
choice        0.43    0.53  0.63
pain          0.36    0.53  0.65
awareness     0.40    0.52  0.62
figuring_out  0.40    0.51  0.57
guilt         0.33    0.50  0.61
temperature   0.38    0.49  0.60
depth         0.25    0.43  0.55
memory        0.29    0.41  0.46

EFA plots

Participant-level analyses

Age group comparison

Thinking continuously

Linear mixed model fit by REML ['lmerMod']
Formula: diff ~ comparison * scale(age, scale = F) + (1 | subid)
   Data: df_endorsements_diff

REML criterion at convergence: 2861.2

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-3.08026 -0.56230  0.02049  0.49809  2.77031 

Random effects:
 Groups   Name        Variance Std.Dev.
 subid    (Intercept) 0.826    0.9088  
 Residual             2.713    1.6471  
Number of obs: 702, groups:  subid, 234

Fixed effects:
                                      Estimate Std. Error t value
(Intercept)                           -0.09402    0.08599  -1.093
comparisonBH_GM                       -0.38034    0.08792  -4.326
comparisonMB_GM                       -0.04701    0.08792  -0.535
scale(age, scale = F)                  0.17740    0.04631   3.830
comparisonBH_GM:scale(age, scale = F) -0.23699    0.04735  -5.005
comparisonMB_GM:scale(age, scale = F)  0.08870    0.04735   1.873

Correlation of Fixed Effects:
            (Intr) cBH_GM cMB_GM s(,s=F cBHs=F
cmprsnBH_GM  0.000                            
cmprsnMB_GM  0.000 -0.500                     
scl(g,sc=F)  0.000  0.000  0.000              
cBH_GM:(s=F  0.000  0.000  0.000  0.000       
cMB_GM:(s=F  0.000  0.000  0.000  0.000 -0.500

Call:
lm(formula = diff ~ scale(age, scale = F), data = df_endorsements_diff %>% 
    filter(comparison == "BODY minus HEART"))

Residuals:
    Min      1Q  Median      3Q     Max 
-4.6524 -0.6719  0.3589  0.6677  4.6555 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -0.47436    0.11072  -4.284 2.69e-05 ***
scale(age, scale = F) -0.05959    0.05963  -0.999    0.319    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.694 on 232 degrees of freedom
  (13 observations deleted due to missingness)
Multiple R-squared:  0.004286,  Adjusted R-squared:  -6.251e-06 
F-statistic: 0.9985 on 1 and 232 DF,  p-value: 0.3187


Call:
lm(formula = diff ~ scale(age, scale = F), data = df_endorsements_diff %>% 
    filter(comparison == "MIND minus BODY"))

Residuals:
    Min      1Q  Median      3Q     Max 
-4.4025 -1.3496 -0.1797  0.7691  5.5504 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -0.14103    0.12899  -1.093 0.275382    
scale(age, scale = F)  0.26610    0.06947   3.830 0.000165 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.973 on 232 degrees of freedom
  (13 observations deleted due to missingness)
Multiple R-squared:  0.05948,   Adjusted R-squared:  0.05543 
F-statistic: 14.67 on 1 and 232 DF,  p-value: 0.0001647


Call:
lm(formula = diff ~ scale(age, scale = F), data = df_endorsements_diff %>% 
    filter(comparison == "MIND minus HEART"))

Residuals:
    Min      1Q  Median      3Q     Max 
-5.7817 -1.0942 -0.0243  1.2580  5.0960 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            0.33333    0.12836   2.597     0.01 *  
scale(age, scale = F)  0.32569    0.06913   4.711 4.24e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.963 on 232 degrees of freedom
  (13 observations deleted due to missingness)
Multiple R-squared:  0.08732,   Adjusted R-squared:  0.08338 
F-statistic:  22.2 on 1 and 232 DF,  p-value: 4.244e-06
Joining, by = c("param", "Estimate", "Std..Error", "t.value", "Pr...t..", "comparison")
Joining, by = c("param", "Estimate", "Std..Error", "t.value", "Pr...t..", "comparison")
Linear mixed model fit by REML ['lmerMod']
Formula: diff_abs ~ comparison * scale(age, scale = F) + (1 | subid)
   Data: df_endorsements_diff

REML criterion at convergence: 2378.6

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.59494 -0.60840 -0.09506  0.53532  2.75598 

Random effects:
 Groups   Name        Variance Std.Dev.
 subid    (Intercept) 0.5669   0.7529  
 Residual             1.2679   1.1260  
Number of obs: 702, groups:  subid, 234

Fixed effects:
                                      Estimate Std. Error t value
(Intercept)                            1.40456    0.06503  21.599
comparisonBH_GM                       -0.14387    0.06010  -2.394
comparisonMB_GM                        0.06980    0.06010   1.161
scale(age, scale = F)                  0.08716    0.03502   2.489
comparisonBH_GM:scale(age, scale = F)  0.02464    0.03237   0.761
comparisonMB_GM:scale(age, scale = F) -0.06013    0.03237  -1.858

Correlation of Fixed Effects:
            (Intr) cBH_GM cMB_GM s(,s=F cBHs=F
cmprsnBH_GM  0.000                            
cmprsnMB_GM  0.000 -0.500                     
scl(g,sc=F)  0.000  0.000  0.000              
cBH_GM:(s=F  0.000  0.000  0.000  0.000       
cMB_GM:(s=F  0.000  0.000  0.000  0.000 -0.500

Call:
lm(formula = diff_abs ~ scale(age, scale = F), data = df_endorsements_diff %>% 
    filter(comparison == "BODY minus HEART"))

Residuals:
    Min      1Q  Median      3Q     Max 
-1.6244 -1.0446 -0.1915  0.7121  3.9771 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            1.26068    0.07902  15.953  < 2e-16 ***
scale(age, scale = F)  0.11180    0.04256   2.627  0.00919 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.209 on 232 degrees of freedom
  (13 observations deleted due to missingness)
Multiple R-squared:  0.02888,   Adjusted R-squared:  0.0247 
F-statistic:   6.9 on 1 and 232 DF,  p-value: 0.009193


Call:
lm(formula = diff_abs ~ scale(age, scale = F), data = df_endorsements_diff %>% 
    filter(comparison == "MIND minus BODY"))

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5618 -1.4221 -0.4329  0.5894  4.4495 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            1.47436    0.09163  16.091   <2e-16 ***
scale(age, scale = F)  0.02703    0.04935   0.548    0.584    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.402 on 232 degrees of freedom
  (13 observations deleted due to missingness)
Multiple R-squared:  0.001291,  Adjusted R-squared:  -0.003013 
F-statistic:   0.3 on 1 and 232 DF,  p-value: 0.5844


Call:
lm(formula = diff_abs ~ scale(age, scale = F), data = df_endorsements_diff %>% 
    filter(comparison == "MIND minus HEART"))

Residuals:
    Min      1Q  Median      3Q     Max 
-1.8730 -1.2235 -0.2740  0.7555  4.3065 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            1.47863    0.09425  15.688   <2e-16 ***
scale(age, scale = F)  0.12266    0.05076   2.416   0.0165 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.442 on 232 degrees of freedom
  (13 observations deleted due to missingness)
Multiple R-squared:  0.02455,   Adjusted R-squared:  0.02034 
F-statistic: 5.838 on 1 and 232 DF,  p-value: 0.01645
Joining, by = c("param", "Estimate", "Std..Error", "t.value", "Pr...t..", "comparison")
Joining, by = c("param", "Estimate", "Std..Error", "t.value", "Pr...t..", "comparison")
Joining, by = c("param", "Estimate", "Std..Error", "t.value", "Pr...t..", "comparison", "diff_type")
Ignoring unknown aesthetics: fill

Supplemental slides

3 age groups

# A tibble: 3 x 6
  tercile     n   min   max  mean median
    <int> <int> <dbl> <dbl> <dbl>  <dbl>
1       1    79  4.00  5.27  4.70   4.68
2       2    79  5.27  7.94  6.62   6.72
3       3    78  7.94  9.99  8.92   8.84
Joining, by = c("capacity", "factor", "loading", "tercile")
Joining, by = c("capacity", "factor", "loading", "tercile")
Joining, by = "capacity"
Joining, by = "capacity"
Joining, by = "capacity"

Attributions

Joining, by = "capacity"

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Using alpha for a discrete variable is not advised.

---
title: "PRESENTATION Weisman, Dweck, & Markman (Cogsci 2018)"
output: 
  html_notebook:
    toc: true
    toc_float: true
---

This is an notebook containing code for generating plots for our talk at Cogsci 2018 (Madison, WI). The corresponding proceedings paper is [here](https://kgweisman.github.io/pub_files/Weisman,%20Dweck,%20&%20Markman%20(2018).pdf) in PDF form, and [here](https://github.com/kgweisman/cogsci2018_dimkid/tree/master/revision) in .Rmd form.

```{r, include = F}
knitr::opts_chunk$set(fig.width=3, fig.height=3, fig.crop = F, fig.pos = "tb", fig.path='figs/', echo=F, warning=F, cache=F, message=F, sanitize = T)
```

```{r libraries, include = F}
# load required packages
library(png)
library(grid)
library(xtable)
library(tidyverse)
library(lubridate)
library(psych)
library(rms)
library(lme4)
```

```{r functions, include = F}
# round to exactly 2 decimal places
round2 <- function(x) {format(round(x, 2), nsmall = 2)}

# determine how many factors meet custom retention criteria
retain_nfactors <- function(df_efa, n_var = 20, 
                       chosen_cor = "cor", chosen_rot = "oblimin") {
  
  # make function for determining max factors to extract (based on df)
  max_fact_fun <- function(p) {
    
    s_moments <- function(p) {p*(p+1)/2}
    param_est <- function(p, k) {p*k + p - (k*(k-1)/2)}
    check_ok <- function(p, k) {
      a <- (p-k)^2
      b <- p+k
      return(ifelse(a>b, TRUE, FALSE))
    }
    
    df_check <- data.frame()
    for(i in 1:p){
      df_check[i,"check"] <- check_ok(p,i)
    }
    
    max <- df_check %>% filter(check) %>% nrow()
    return(max)
    
  }
  
  # do maximal efa
  nfact_max <- max_fact_fun(n_var)
  efa_max_unrot <- psych::fa(df_efa, nfactors = nfact_max, 
                             cor = chosen_cor, rotate = "none")
  
  # keep factors with eigenvalues > 1, proportion var explained > 5%
  nfact_keep_mid <- efa_max_unrot$Vaccounted %>%
    t() %>%
    data.frame() %>%
    rownames_to_column("factor") %>%
    filter(SS.loadings > 1, Proportion.Explained > 0.05) %>%
    nrow()
  
  # do efa with nfact_keep_mid factors + rotation
  efa_mid_rot <- psych::fa(df_efa, nfactors = nfact_keep_mid, 
                           cor = chosen_cor, rotate = chosen_rot)
  
  # keep factors that are dominant for >= 1 item
  nfact_keep_final <- efa_mid_rot$loadings[] %>%
    data.frame() %>%
    rownames_to_column("capacity") %>%
    gather(factor, loading, -capacity) %>%
    group_by(capacity) %>%
    top_n(1, abs(loading)) %>%
    ungroup() %>%
    count(factor) %>%
    nrow()
  
  return(nfact_keep_final)
  
}

# print top n dominant items by factor
top_n_domCap <- function(loadings_df, n, factor){
  dom_df <- loadings_df %>%
    full_join(d_all %>% distinct(capacity, capWording)) %>%
    gather(factor, loading, -capacity, -capWording) %>%
    group_by(capacity, capWording) %>%
    top_n(1, abs(loading)) %>%
    ungroup() %>%
    group_by(factor) %>%
    top_n(n, abs(loading))
  
  wordings <- dom_df$capWording[dom_df$factor == factor] %>% 
    paste(collapse = ", ")
  
  return(wordings)
  
}
```

```{r choices, include = F}
# what correlation to use
chosen_cor <- "cor" # reported in paper
# chosen_cor <- "poly" # alternative option

# what rotation to use
chosen_rot <- "oblimin" # reported in paper
# chosen_rot <- "varimax" # alternative option

# number of iterations for efa
n_iter <- 10
# n_iter <- 5000
```

```{r load data, include = F, warning = F}
# older children (7-9y)
d_raw_old <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/children/run-02_2017-08-08_anonymized.csv") %>%
  mutate(age_group = "children_79") %>%
  select(-X, -trial.comments, -trialComments, -sessionComments)

# younger children (4-6y)
d_raw_young <- read.csv("/Users/kweisman/Documents/Research (Stanford)/Projects/Dimkid/dimkid/data/children/run-03_2017-08-21_anonymized.csv") %>%
  mutate(age_group = "children_46") %>%
  select(-X, -trial.comments, -trialComments, -sessionComments)

d_raw <- d_raw_old %>% 
  full_join(d_raw_young) %>%
  mutate(dob = parse_datetime(dateOfBirth, "%m/%d/%y"),
         dot = parse_datetime(gsub("2017", "17", dateOfTest), "%m/%d/%y"), 
         age = interval(start = dob, end = dot) / 
           duration(num = 1, units = "years")) %>%
  select(-dateOfBirth, -dateOfTest, -dob, -dot)
```

```{r tidy data, include = F, warning = F}
# implement filters
d0 <- d_raw %>%
  filter(trialNum <= 20) %>%
  mutate(response = tolower(response),
         age_group = ifelse(is.na(age), age_group, # re-sort as needed
                            ifelse(age < 7, "children_46", "children_79"))) %>%
  filter((age >= 4 & age < 10) | is.na(age), # outside of age range
         (rt >= 250 | is.na(rt)), # fast RTs
         response %in% c("no", "kinda", "yes")) # skipped trials

# recode variables
d1 <- d0 %>%
  mutate(capWording = gsub(" $", "", capWording),
         capWording = gsub(" -- ", "--", capWording),
         capacity = recode(capWording,
                           "be aware of things" = "awareness",
                           "feel embarrassed" = "embarrassment",
                           "feel guilty" = "guilt",
                           "feel happy" = "happiness",
                           "feel love" = "love",
                           "feel pain" = "pain",
                           "feel proud" = "pride",
                           "feel sad" = "sadness",
                           "feel scared" = "fear",
                           "feel sick--like when you feel like you might throw up" = "nausea",
                           "feel tired" = "fatigue",
                           "figure out how to do things" = "figuring_out",
                           "get angry" = "anger",
                           "get hungry" = "hunger",
                           "get hurt feelings" = "hurt_feelings",
                           "make choices" = "choice",
                           "remember things" = "memory",
                           "sense temperatures" = "temperature",
                           "sense whether something is close by or far away" = "depth",
                           "smell things" = "smell"),
         responseNum = recode(response, "no" = 0, "kinda" = 0.5, "yes" = 1),
         character = factor(character,
                            levels = c("elephant", "goat", "mouse", "bird",
                                       "beetle", "teddy_bear", "doll",
                                       "robot", "computer")),
         testingSite = tolower(testingSite),
         testingSiteType = recode(testingSite,
                                  "bing" = "preschool",
                                  "jmz" = "museum",
                                  "tech" = "museum")) %>%
  distinct()

# separate by age group
d_all <- d1
d_old <- d1 %>% filter(age_group == "children_79")
d_young <- d1 %>% filter(age_group == "children_46")

# make wideform versions for EFA
d_old_wide <- d_old %>%
  distinct(subid, capacity, responseNum) %>%
  spread(capacity, responseNum) %>%
  remove_rownames() %>%
  column_to_rownames("subid")

d_young_wide <- d_young %>%
  distinct(subid, capacity, responseNum) %>%
  spread(capacity, responseNum) %>%
  remove_rownames() %>%
  column_to_rownames("subid")

# rm(d_raw, d_raw_old, d_raw_young, d0, d1)
```

```{r participants, include = F}
# n
n_total <- data.frame(d_all %>% distinct(subid) %>% count())$n
n_old <- data.frame(d_old %>% distinct(subid) %>% count())$n
n_young <- data.frame(d_young %>% distinct(subid) %>% count())$n

# age
age_median_old <- median(d_old$age, na.rm = T)
age_min_old <- min(d_old$age, na.rm = T)
age_max_old <- max(d_old$age, na.rm = T)
age_median_young <- median(d_young$age, na.rm = T)
age_min_young <- min(d_young$age, na.rm = T)
age_max_young <- max(d_young$age, na.rm = T)

# study duration
duration_median_old <- median(d_old$sessionDuration, na.rm = T)
duration_median_young <- median(d_young$sessionDuration, na.rm = T)

# site
site_df <- d_all %>%
  distinct(age_group, subid, testingSiteType) %>%
  count(age_group, testingSiteType) %>%
  group_by(age_group) %>%
  mutate(prop = n/sum(n)) %>%
  data.frame()

# character
character_df <- d_all %>%
  distinct(age_group, subid, character) %>%
  count(age_group, character) %>%
  data.frame()

# rt < 250ms
rt_df <- d_raw %>%
  distinct(age_group, subid, trialNum, rt) %>%
  mutate(rt_fast = ifelse(is.na(rt), "ok", ifelse(rt < 250, "fast", "ok")),
         rt_fast = factor(rt_fast, levels = c("ok", "fast"))) %>%
  count(age_group, rt_fast) %>%
  complete(rt_fast, nesting(age_group), fill = list(n = 0)) %>%
  data.frame()

# skipped trials
skip_df <- d_all %>%
  complete(capacity, nesting(subid, age_group), 
           fill = list(response = "SKIP")) %>%
  distinct(age_group, subid, capacity, response) %>%
  mutate(response = factor(response,
                           levels = c("no", "kinda", "yes", "SKIP"))) %>%
  count(age_group, response) %>% 
  group_by(age_group) %>%
  mutate(prop = n/sum(n)) %>%
  data.frame()
```

# EFA calculations

## Older children (7-9y)

```{r efa old, warnings = FALSE}
# determine how many factors to extract
nfactors_old <- retain_nfactors(df_efa = d_old_wide)

# alternative factor retention methods: uncomment to run
# fa.parallel(d_old_wide, fa = "fa", n.iter = n_iter)
# VSS(d_old_wide)

# do EFA
efa_old <- psych::fa(d_old_wide, nfactors = nfactors_old, n.iter = n_iter,
                     cor = chosen_cor, rot = chosen_rot) %>% fa.sort()
colnames(efa_old$loadings) <- paste("factor", 1:nfactors_old, sep = "")

# get useful info from EFA
efa_old_loadings <- efa_old$loadings[] %>% 
  data.frame() %>%
  rownames_to_column("capacity")

efa_old_variance <- efa_old$Vaccounted %>% 
  t() %>%
  data.frame() %>%
  mutate(factor = paste("factor", 1:nfactors_old, sep = ""))

# efa_old_correlations <- efa_old$score.cor %>%
#   data.frame() %>%
#   rename(factor1 = X1, factor2 = X2, factor3 = X3) %>%
#   mutate(factorA = paste("factor", 1:nfactors_old, sep = "")) %>%
#   gather(factorB, cor, -factorA)

efa_old
```

## Younger children (4-6y)

```{r efa young, warnings = FALSE}
# determine how many factors to extract
nfactors_young <- retain_nfactors(df_efa = d_young_wide)

# alternative factor retention methods: uncomment to run
# fa.parallel(d_young_wide, fa = "fa", n.iter = n_iter)
# VSS(d_young_wide)

# do EFA
efa_young <- psych::fa(d_young_wide, nfactors = nfactors_young, n.iter = n_iter,
                     cor = chosen_cor, rot = chosen_rot) %>% fa.sort()
colnames(efa_young$loadings) <- paste("factor", 1:nfactors_young, sep = "")

# get useful info from EFA
efa_young_loadings <- efa_young$loadings[] %>% 
  data.frame() %>%
  rownames_to_column("capacity")

efa_young_variance <- efa_young$Vaccounted %>% 
  t() %>%
  data.frame() %>%
  mutate(factor = paste("factor", 1:nfactors_young, sep = ""))

efa_young_correlations <- efa_young$score.cor %>%
  data.frame()
colnames(efa_young_correlations) <- paste("factor", 1:nfactors_young, sep = "")
efa_young_correlations <- efa_young_correlations %>%
  mutate(factorA = paste("factor", 1:nfactors_young, sep = "")) %>%
  gather(factorB, cor, -factorA)

# calculate congruence with older kids' factors
efa_young_congruence <- factor.congruence(efa_old, efa_young) %>%
  data.frame() %>%
  rownames_to_column("old_factor") %>%
  gather(young_factor, congruence, -old_factor)

efa_young
```

```{r efa young force 2 factors, warnings = FALSE}
# do EFA, forcibly extracting 2 factors
efa_young_force2 <- psych::fa(d_young_wide, nfactors = 2, n.iter = n_iter,
                     cor = chosen_cor, rot = chosen_rot) %>% fa.sort()
colnames(efa_young_force2$loadings) <- paste("factor", 1:2, sep = "")

# get useful info from EFA
efa_young_force2_loadings <- efa_young_force2$loadings[] %>% 
  data.frame() %>%
  rownames_to_column("capacity")

efa_young_force2_variance <- efa_young_force2$Vaccounted %>% 
  t() %>%
  data.frame() %>%
  mutate(factor = paste("factor", 1:2, sep = ""))

efa_young_force2_correlations <- efa_young_force2$score.cor %>%
  data.frame()
colnames(efa_young_force2_correlations) <- paste("factor", 1:2, sep = "")
efa_young_force2_correlations <- efa_young_force2_correlations %>%
  mutate(factorA = paste("factor", 1:2, sep = "")) %>%
  gather(factorB, cor, -factorA)

# calculate congruence with older kids' factors
efa_young_force2_congruence <- factor.congruence(efa_old, efa_young_force2) %>%
  data.frame() %>%
  rownames_to_column("old_factor") %>%
  gather(young_force2_factor, congruence, -old_factor)

efa_young_force2
```

```{r efa young force 1 factor, warnings = FALSE}
# do EFA, forcibly extracting 1 factor
efa_young_force1 <- psych::fa(d_young_wide, nfactors = 1, n.iter = n_iter,
                     cor = chosen_cor, rot = chosen_rot) %>% fa.sort()
colnames(efa_young_force1$loadings) <- paste("factor", 1, sep = "")

# get useful info from EFA
efa_young_force1_loadings <- efa_young_force1$loadings[] %>% 
  data.frame() %>%
  rownames_to_column("capacity")

efa_young_force1_variance <- efa_young_force1$Vaccounted %>% 
  t() %>%
  data.frame() %>%
  mutate(factor = paste("factor", 1, sep = ""))

# efa_young_force1_correlations <- efa_young_force1$score.cor %>%
#   data.frame()
# colnames(efa_young_force1_correlations) <- paste("factor", 1, sep = "")
# efa_young_force1_correlations <- efa_young_force1_correlations %>%
#   mutate(factorA = paste("factor", 1, sep = "")) %>%
#   gather(factorB, cor, -factorA)

# calculate congruence with older kids' factors
efa_young_force1_congruence <- factor.congruence(efa_old, efa_young_force1) %>%
  data.frame() %>%
  rownames_to_column("old_factor") %>%
  gather(young_force1_factor, congruence, -old_factor)

efa_young_force1
```

# EFA plots

```{r}
order_old <- efa_old_loadings %>% 
  gather(factor, loading, -capacity) %>% 
  group_by(capacity) %>% 
  top_n(1, abs(loading)) %>% 
  ungroup() %>% 
  rownames_to_column("order_old") %>% 
  mutate(order_old = as.numeric(order_old)) %>%
  select(capacity, order_old)

order_young3 <- efa_young_loadings %>% 
  gather(factor, loading, -capacity) %>% 
  group_by(capacity) %>% 
  top_n(1, abs(loading)) %>% 
  ungroup() %>% 
  rownames_to_column("order_young3") %>% 
  mutate(order_young3 = as.numeric(order_young3)) %>%
  select(capacity, order_young3)

order_young2 <- efa_young_force2_loadings %>% 
  gather(factor, loading, -capacity) %>% 
  group_by(capacity) %>% 
  top_n(1, abs(loading)) %>% 
  ungroup() %>% 
  rownames_to_column("order_young2") %>% 
  mutate(order_young2 = as.numeric(order_young2)) %>%
  select(capacity, order_young2)

order_young1 <- efa_young_force1_loadings %>% 
  gather(factor, loading, -capacity) %>% 
  group_by(capacity) %>% 
  top_n(1, abs(loading)) %>% 
  ungroup() %>% 
  rownames_to_column("order_young1") %>% 
  mutate(order_young1 = as.numeric(order_young1)) %>%
  select(capacity, order_young1)
```

```{r plot prep, include = F}
figure1_df <- efa_old_loadings %>% 
  rename(old_BODY = factor1, old_HEART = factor2, old_MIND = factor3) %>%
  full_join(efa_young_loadings %>%
              rename(young_BODY = factor1, young_HEART = factor2, 
                     young_MIND = factor3)) %>%
  full_join(efa_young_force2_loadings %>%
              rename(forced1 = factor1, forced2 = factor2)) %>%
  gather(factor, loading, -capacity) %>%
  mutate(factor = factor(factor,
                         levels = c("old_BODY", "old_HEART", "old_MIND",
                                    "young_BODY", "young_HEART", "young_MIND",
                                    "forced1", "forced2"),
                         labels = c("7-9y\n3-factors:\nBODY", 
                                    "7-9y\n3-factors:\nHEART", 
                                    "7-9y\n3-factors:\nMIND", 
                                    "4-6y\n3-factors:\nBODY",
                                    "4-6y\n3-factors:\nHEART",
                                    "4-6y\n3-factors:\nMIND",
                                    "4-6y\n2-factors:\nBODY-HEART",
                                    "4-6y\n2-factors:\nMIND"))) %>%
  full_join(d_all %>% distinct(capacity, capWording)) %>%
  # mutate(capWording = ifelse(grepl("feel sick", capWording), 
  #                            "feel sick... throw up", capWording),
  #        capWording = ifelse(grepl("far away", capWording), 
  #                            "sense... far away", capWording),
  #        capWording = ifelse(grepl("figure out", capWording), 
  #                            "figure out...", capWording)) %>%
  full_join(order_old) %>%
  full_join(order_young3) %>%
  full_join(order_young2) %>%
  full_join(order_young1)

var_df <- efa_old_variance %>% 
  mutate(factor = recode(factor,
                         "factor1" = "7-9y\n3-factors:\nBODY",
                         "factor2" = "7-9y\n3-factors:\nHEART",
                         "factor3" = "7-9y\n3-factors:\nMIND")) %>% 
  full_join(efa_young_variance %>% 
              mutate(factor = recode(factor,
                                     "factor1" = "4-6y\n3-factors:\nBODY",
                                     "factor2" = "4-6y\n3-factors:\nHEART",
                                     "factor3" = "4-6y\n3-factors:\nMIND"))) %>% 
  full_join(efa_young_force2_variance %>% 
              mutate(factor = recode(factor,
                                     "factor1" = "4-6y\n2-factors:\nBODY-HEART",
                                     "factor2" = "4-6y\n2-factors:\nMIND")))
```

```{r efa_old plot, fig.width = 6, fig.asp = 0.8}
figure1_df %>%
  filter(grepl("7-9y\n3-factors", factor)) %>%
  ggplot(aes(x = factor, y = reorder(capWording, desc(order_old)), fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 3.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  geom_text(data = var_df %>% filter(grepl("7-9y\n3-factors", factor)),
            size = 6,
            aes(x = factor, y = 0, fill = NULL,
                label = paste0(round(Proportion.Explained, 2)*100, "%"))) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 30, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```

```{r efa_young3 plot, fig.width = 6, fig.asp = 0.8}
figure1_df %>%
  filter(grepl("4-6y\n3-factors", factor)) %>%
  ggplot(aes(x = factor, y = reorder(capWording, desc(order_young3)), fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 3.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  geom_text(data = var_df %>% filter(grepl("4-6y\n3-factors", factor)),
            size = 6,
            aes(x = factor, y = 0, fill = NULL,
                label = paste0(round(Proportion.Explained, 2)*100, "%"))) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 30, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```

```{r efa_young2 plot, fig.width = 6, fig.asp = 0.8}
figure1_df %>%
  filter(grepl("4-6y\n2-factors", factor)) %>%
  ggplot(aes(x = factor, y = reorder(capWording, desc(order_young2)), fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 2.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  geom_text(data = var_df %>% filter(grepl("4-6y\n2-factors", factor)),
            size = 6,
            aes(x = factor, y = 0, fill = NULL,
                label = paste0(round(Proportion.Explained, 2)*100, "%"))) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 30, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```

# Participant-level analyses

```{r endorsements, include = F}
df_factors <- efa_old_loadings %>%
  gather(factor, loading, -capacity) %>%
  group_by(capacity) %>%
  top_n(1, abs(loading)) %>%
  ungroup() %>%
  group_by(factor) %>%
  top_n(6, abs(loading)) %>%
  ungroup() %>%
  mutate(factor = recode(factor,
                         "factor1" = "BODY",
                         "factor2" = "HEART",
                         "factor3" = "MIND"))

df_endorsements <- d_all %>%
  full_join(df_factors) %>%
  filter(!is.na(factor)) %>%
  group_by(age_group, subid, character, age, factor) %>%
  mutate(endorse = recode(response,
                          "no" = 0,
                          "kinda" = 1,
                          "yes" = 1)) %>%
  summarise(total = sum(endorse, na.rm = T))

df_endorsements_diff <- df_endorsements %>%
  spread(factor, total) %>%
  mutate(HEART_BODY = HEART - BODY,
         MIND_BODY = MIND - BODY,
         MIND_HEART = MIND - HEART) %>%
  select(-c(BODY, HEART, MIND)) %>%
  gather(comparison, diff, c(HEART_BODY, MIND_BODY, MIND_HEART)) %>%
  mutate(comparison = factor(comparison,
                             labels = c("BODY minus HEART",
                                        "MIND minus BODY",
                                        "MIND minus HEART")),
         diff_abs = abs(diff))
```

## Age group comparison

```{r table 1 prep}
diff_tab <- df_endorsements_diff %>%
  ungroup() %>%
  # mutate(age_group = factor(age_group, labels = c("4-6y", "7-9y")),
  #        comparison = gsub("minus", "-", comparison)) %>%
  group_by(age_group, comparison) %>%
  summarise(n = n(),
            median = median(diff),
            mean = mean(diff, na.rm = T),
            variance = var(diff, na.rm = T),
            skewness = psych::skew(diff),
            kurtosis = psych::kurtosi(diff)) %>%
  mutate_at(vars(mean, variance, skewness, kurtosis), funs(round2)) %>%
  # mutate(comparison = factor(comparison,
  #                            labels = c("BODY minus HEART", 
  #                                       "BODY minus MIND", 
  #                                       "MIND minus HEART"))) %>%
  ungroup() %>% 
  arrange(comparison, age_group) %>%
  select(comparison, age_group, n, median, mean, variance, skewness, kurtosis) %>%
  data.frame()
```

```{r Table 1 prep}
# wilcoxon tests
w1 <- wilcox.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "BODY minus HEART"))
w2 <- wilcox.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "MIND minus BODY"))
w3 <- wilcox.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "MIND minus HEART"))

# welch's tests
t1 <- t.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "BODY minus HEART"))
t2 <- t.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "MIND minus BODY"))
t3 <- t.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "MIND minus HEART"))

# bartlett's tests
ksq1 <- bartlett.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "BODY minus HEART"))
ksq2 <- bartlett.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "MIND minus BODY"))
ksq3 <- bartlett.test(diff ~ age_group, df_endorsements_diff %>% filter(comparison == "MIND minus HEART"))

difftests_tab <- data.frame(group = c("B-H", "M-B", "M-H"),
                            W = c(w1$statistic, w2$statistic, w3$statistic),
                            Wp = c(w1$p.value, w2$p.value, w3$p.value),
                            t = c(t1$statistic, t2$statistic, t3$statistic),
                            tp = c(t1$p.value, t2$p.value, t3$p.value),
                            K2 = c(ksq1$statistic, ksq2$statistic, 
                                   ksq3$statistic),
                            K2p = c(ksq1$p.value, ksq2$p.value, 
                                    ksq3$p.value)) %>%
  mutate_at(vars(-group), funs(round2))

names(difftests_tab) <- c("", "W", "p", "t", "p", "K^2", "p")
```

```{r}
df_endorsements_diff %>% 
  group_by(comparison, age_group) %>% 
  summarise(mean = mean(diff),
            var = var(diff)) %>%
  mutate_at(vars(var, mean), funs(. %>% round(2) %>% format(nmall = 2)))
```

```{r endorsements plot, fig.width = 6, fig.asp = 0.67}
ggplot(df_endorsements_diff %>%
         ungroup() %>%
         mutate(age_group = factor(age_group,
                                   levels = c("children_79", "children_46"),
                                   labels = c("7-9y", "4-6y"))),
       aes(x = diff, fill = age_group, color = age_group)) +
  facet_grid(age_group ~ comparison) +
  geom_bar(position = position_identity(), alpha = 0.5, size = 0.5) +
  geom_vline(xintercept = 0, lty = 2) +
  geom_text(data = diff_tab %>% 
              mutate(age_group = factor(age_group,
                                        levels = c("children_79", "children_46"),
                                   labels = c("7-9y", "4-6y"))), 
            aes(label = paste("M =", mean)),
            x = -7, y = 42, hjust = 0, vjust = 0, size = 7) +
  geom_text(data = diff_tab %>% 
              mutate(age_group = factor(age_group,
                                        levels = c("children_79", "children_46"),
                                   labels = c("7-9y", "4-6y"))), 
            aes(label = paste("s =", variance)),
            x = 7, y = 42, hjust = 1, vjust = 0, size = 7) +
  scale_x_continuous("Difference between categories", 
                     limits = c(-7, 7), breaks = seq(-6, 6, 2)) +
  scale_y_continuous("Number of participants", breaks = seq(0, 100, 10)) +
  scale_fill_manual("Age group",
                    values = c("#7fbf7b", "#af8dc3")) +
  scale_color_manual("Age group", 
                     values = c("#008837", "#7b3294")) +
  theme_minimal() +
  guides(fill = guide_legend(override.aes = list(alpha = 1)),
         color = guide_legend(override.aes = list(size = 1))) +
  theme(legend.position = "none",
        text = element_text(size = 24),
        panel.border = element_rect(fill = NA),
        panel.grid.minor = element_blank())
```

## Thinking continuously

```{r}
contrasts(df_endorsements_diff$comparison) <- cbind(BH_GM = c(1, 0, -1),
                                                    MB_GM = c(0, 1, -1))
```

```{r}
r_raw_all <- lmer(diff ~ comparison * scale(age, scale = F) + (1|subid),
                  df_endorsements_diff)
summary(r_raw_all)

r_raw_BH <- lm(diff ~ scale(age, scale = F),
               df_endorsements_diff %>% filter(comparison == "BODY minus HEART"))
summary(r_raw_BH)

r_raw_MB <- lm(diff ~ scale(age, scale = F),
               df_endorsements_diff %>% filter(comparison == "MIND minus BODY"))
summary(r_raw_MB)

r_raw_MH <- lm(diff ~ scale(age, scale = F),
               df_endorsements_diff %>% filter(comparison == "MIND minus HEART"))
summary(r_raw_MH)

regressions_raw <- data.frame(summary(r_raw_BH)$coefficients) %>%
  rownames_to_column("param") %>%
  mutate(comparison = "BODY minus HEART") %>%
  full_join(data.frame(summary(r_raw_MB)$coefficients) %>%
              rownames_to_column("param") %>%
              mutate(comparison = "MIND minus BODY")) %>%
  full_join(data.frame(summary(r_raw_MH)$coefficients) %>%
              rownames_to_column("param") %>%
              mutate(comparison = "MIND minus HEART"))
```

```{r}
r_abs_all <- lmer(diff_abs ~ comparison * scale(age, scale = F) + (1|subid),
                  df_endorsements_diff)
summary(r_abs_all)

r_abs_BH <- lm(diff_abs ~ scale(age, scale = F),
               df_endorsements_diff %>% filter(comparison == "BODY minus HEART"))
summary(r_abs_BH)

r_abs_MB <- lm(diff_abs ~ scale(age, scale = F),
               df_endorsements_diff %>% filter(comparison == "MIND minus BODY"))
summary(r_abs_MB)

r_abs_MH <- lm(diff_abs ~ scale(age, scale = F),
               df_endorsements_diff %>% filter(comparison == "MIND minus HEART"))
summary(r_abs_MH)

regressions_abs <- data.frame(summary(r_abs_BH)$coefficients) %>%
  rownames_to_column("param") %>%
  mutate(comparison = "BODY minus HEART") %>%
  full_join(data.frame(summary(r_abs_MB)$coefficients) %>%
              rownames_to_column("param") %>%
              mutate(comparison = "MIND minus BODY")) %>%
  full_join(data.frame(summary(r_abs_MH)$coefficients) %>%
              rownames_to_column("param") %>%
              mutate(comparison = "MIND minus HEART"))
```

```{r}
regressions_all <- full_join(regressions_raw %>% 
                               mutate(diff_type = "raw difference"),
                             regressions_abs %>%
                               mutate(diff_type = "absolute difference")) %>%
  filter(param == "scale(age, scale = F)") %>%
  select(-param) %>%
  rename(b = Estimate,
         b_se = Std..Error,
         t = t.value,
         p = Pr...t..) %>%
  mutate_at(vars(b, b_se, t),
            funs(. %>% round(2) %>% format(nsmall = 2))) %>%
  mutate(p = ifelse(p < 0.001, "p < 0.001",
                    paste0("p = ", format(round(p, 3), nsmall = 3))),
         diff_type = factor(diff_type, 
                            levels = c("raw difference", "absolute difference")))
```

```{r endorsements plot continuous, fig.width = 6, fig.asp = 0.75}
ggplot(df_endorsements_diff %>%
         ungroup() %>%
         mutate(age_group = factor(age_group,
                                   levels = c("children_79", "children_46"),
                                   labels = c("7-9y", "4-6y"))) %>%
         gather(diff_type, diff_deg, c(diff, diff_abs)) %>%
         mutate(diff_type = factor(diff_type,
                                   levels = c("diff", "diff_abs"),
                                   labels = c("raw difference", "absolute difference"))),
       aes(x = age, y = diff_deg, fill = age_group, color = age_group)) +
  facet_grid(diff_type ~ comparison, scale = "free") +
  geom_hline(yintercept = 0, lty = 2) +
  geom_jitter(height = 0.25, width = 0) +
  geom_smooth(aes(group = comparison), method = "lm",
              color = "black", fill = "black", alpha = 0.25) +
  geom_text(data = regressions_all,
            aes(label = paste0("b = ", b, ", ", p), color = NA, fill = NA),
            x = 4, y = 6, color = "black", hjust = 0, vjust = 1, size = 6) +
  scale_x_continuous("Exact age in years", breaks = seq(0, 100, 1)) +
  scale_y_continuous("Difference between categories",
                     breaks = seq(-6, 6, 2)) +
  scale_fill_manual("Age group",
                    values = c("#7fbf7b", "#af8dc3")) +
  scale_color_manual("Age group", 
                     values = c("#008837", "#7b3294")) +
  theme_minimal() +
  guides(fill = guide_legend(override.aes = list(alpha = 1)),
         color = guide_legend(override.aes = list(size = 1))) +
  theme(legend.position = "none",
        text = element_text(size = 24),
        panel.border = element_rect(fill = NA),
        panel.grid.minor = element_blank())  
```

# Supplemental slides

## 3 age groups

```{r}
# split data
d_terciles <- d_all %>%
  filter(!is.na(age)) %>%
  mutate(tercile = ntile(age, 3)) %>%
  select(subid, age, tercile, capacity, responseNum) %>%
  spread(capacity, responseNum)

d_tercile_young <- d_terciles %>% 
  filter(tercile == 1) %>%
  column_to_rownames("subid") %>%
  select(-tercile, -age)

d_tercile_mid <- d_terciles %>% 
  filter(tercile == 2) %>%
  column_to_rownames("subid") %>%
  select(-tercile, -age)

d_tercile_old <- d_terciles %>% 
  filter(tercile == 3) %>%
  column_to_rownames("subid") %>%
  select(-tercile, -age)
```

```{r}
d_terciles %>% 
  distinct(tercile, subid, age) %>% 
  group_by(tercile) %>% 
  summarise(n = n(),
            min = min(age),
            max = max(age),
            mean = mean(age),
            median = median(age))
```


```{r}
# do EFAs
efa_tercile_young <- psych::fa(d_tercile_young, nfactors = 3, #n.iter = n_iter,
                               cor = chosen_cor, rot = chosen_rot) %>% fa.sort()
efa_tercile_mid <- psych::fa(d_tercile_mid, nfactors = 3, #n.iter = n_iter,
                             cor = chosen_cor, rot = chosen_rot) %>% fa.sort()
efa_tercile_old <- psych::fa(d_tercile_old, nfactors = 3, #n.iter = n_iter,
                             cor = chosen_cor, rot = chosen_rot) %>% fa.sort()

order_tercile_young <- efa_tercile_young$loadings[] %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  group_by(capacity) %>%
  top_n(1, abs(loading)) %>%
  ungroup() %>%
  arrange(factor, desc(abs(loading))) %>%
  rownames_to_column("order_young") %>%
  mutate(order_young = as.numeric(order_young)) %>%
  select(order_young, capacity)

order_tercile_mid <- efa_tercile_mid$loadings[] %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  group_by(capacity) %>%
  top_n(1, abs(loading)) %>%
  ungroup() %>%
  arrange(factor, desc(abs(loading))) %>%
  rownames_to_column("order_mid") %>%
  mutate(order_mid = as.numeric(order_mid)) %>%
  select(order_mid, capacity)

order_tercile_old <- efa_tercile_old$loadings[] %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  group_by(capacity) %>%
  top_n(1, abs(loading)) %>%
  ungroup() %>%
  arrange(factor, desc(abs(loading))) %>%
  rownames_to_column("order_old") %>%
  mutate(order_old = as.numeric(order_old)) %>%
  select(order_old, capacity)

efa_tercile_loadings <- efa_tercile_young$loadings[] %>%
  data.frame() %>%
  rownames_to_column("capacity") %>%
  gather(factor, loading, -capacity) %>%
  mutate(tercile = "young") %>%
  full_join(efa_tercile_mid$loadings[] %>%
              data.frame() %>%
              rownames_to_column("capacity") %>%
              gather(factor, loading, -capacity) %>%
              mutate(tercile = "mid")) %>%
  full_join(efa_tercile_old$loadings[] %>%
              data.frame() %>%
              rownames_to_column("capacity") %>%
              gather(factor, loading, -capacity) %>%
              mutate(tercile = "old")) %>%
  full_join(order_tercile_young) %>%
  full_join(order_tercile_mid) %>%
  full_join(order_tercile_old) %>%
  mutate(tercile = factor(tercile, levels = c("young", "mid", "old")))
```

```{r tercile_young plot, fig.width = 4, fig.asp = 1}
ggplot(efa_tercile_loadings %>% filter(tercile == "young"),
       aes(x = factor,
           y = reorder(capacity, desc(order_young)),
           fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 3.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  # expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        # axis.text.x = element_text(angle = 45, hjust = 0, vjust = 0),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```

```{r tercile_mid plot, fig.width = 4, fig.asp = 1}
ggplot(efa_tercile_loadings %>% filter(tercile == "mid"),
       aes(x = factor,
           y = reorder(capacity, desc(order_mid)),
           fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 3.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  # expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        # axis.text.x = element_text(angle = 45, hjust = 0, vjust = 0),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```

```{r tercile_old plot, fig.width = 4, fig.asp = 1}
ggplot(efa_tercile_loadings %>% filter(tercile == "old"),
       aes(x = factor,
           y = reorder(capacity, desc(order_old)),
           fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 3.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 20, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  # expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        # axis.text.x = element_text(angle = 45, hjust = 0, vjust = 0),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```

```{r tercile_all plot, fig.width = 8, fig.asp = 0.7}
ggplot(efa_tercile_loadings,
       aes(x = interaction(factor, tercile),
           y = reorder(capacity, desc(order_old)),
           fill = loading)) +
  geom_tile(color = "black") +
  geom_text(aes(label = round2(loading)), size = 5) +
  annotate("rect", xmin = 0.5, xmax = 3.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  annotate("rect", xmin = 3.5, xmax = 6.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  annotate("rect", xmin = 6.5, xmax = 9.5, ymin = 0.5, ymax = 20.5,
           color = "black", alpha = 0, size = 0.6) +
  scale_fill_distiller(palette = "RdYlBu", 
                       limits = c(-1, 1), breaks = seq(-1, 1, 0.5),
                       guide = guide_colorbar(title = element_blank(),
                                              barheight = 30, barwidth = 1)) +
  scale_x_discrete(position = "top") +
  # expand_limits(y = c(-1, 21)) +
  theme_minimal() +
  labs(x = "") +
  theme(title = element_text(hjust = 0.5),
        text = element_text(size = 24),
        # axis.text.x = element_text(angle = 45, hjust = 0, vjust = 0),
        axis.text.x = element_blank(),
        axis.title.y = element_blank(),
        panel.grid = element_blank())
```


## Attributions

```{r, fig.width = 4, fig.asp = 0.75}
efa_old_loadings %>%
  gather(factor, loading, -capacity) %>%
  group_by(capacity) %>%
  top_n(1, abs(loading)) %>%
  ungroup() %>%
  arrange(factor, desc(abs(loading))) %>%
  rownames_to_column("order") %>%
  mutate(order = as.numeric(order)) %>%
  select(-loading) %>%
  full_join(d_all) %>%
  group_by(age_group, character, factor, capacity, order) %>%
  do(data.frame(rbind(smean.cl.boot(.$responseNum)))) %>%
  ungroup() %>%
  mutate(character = factor(gsub("_", " ", character),
                            levels = c("doll", "teddy bear", "robot", 
                                       "computer", "beetle", "bird", 
                                       "mouse", "goat", "elephant"))) %>%
  ggplot(aes(y = Mean, x = reorder(gsub("_", " ", capacity), order),
             color = factor, alpha = age_group, shape = age_group)) +
  facet_wrap(~ character, ncol = 3) +
  geom_pointrange(aes(ymin = Lower, ymax = Upper),
                  position = position_dodge(width = 0.8)) +
  scale_x_discrete("") +
  scale_y_continuous("Mean response", 
                     breaks = c(0, 0.5, 1), 
                     labels = c("0 (no)", "0.5 (kinda)", "1 (yes)")) +
  scale_color_brewer("Factor", palette = "Set1", 
                     labels = c("BODY", "HEART", "MIND")) +
  scale_alpha_discrete("Age group", range = c(1, 0.5),
                       labels = c("4-6y", "7-9y")) +
  scale_shape_discrete("Age group", labels = c("4-6y", "7-9y")) +
  theme_minimal() +
  theme(panel.border = element_rect(fill = NA),
        axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
        legend.position = "bottom")
```

